Please help! Answer this correctly Moderators ans teachers plz help in these questions please!!
Answers
Solution :
According to the Commutative property
Addition : a + b = b + a
Multiplication : a × b = b × a
★Point to be noted
Commutative property is not applicable for subtraction and division
- For rational number
Addition
→ a = 2/3 and b = 1/2
→ 2/3 + 1/2 = 1/2 + 2/3
→ 4 + 3/6 = 3 + 4/6
→ 7/6 = 7/6
Multiplication
→ a = 2/3 and b = 1/2
→ 2/3 × 1/2 = 1/2 × 2/3
→ 1/3 = 1/3
- For integer
Addition
→ a = 2 and b = - 3
→ 2 + (-3) = - 3 + 2
→ 2 - 3 = - 3 + 2
→ - 1 = - 1
Multiplication
→ a = 2 and b = - 3
→ 2 × (-3) = (-3) × 2
→ - 6 = - 6
- For whole number
Addition
→ a = 2 and b = 0
→ 2 + 0 = 0 + 2
→ 2 = 2
Multiplication
→ a = 2 and b = 0
→ 2 × 0 = 0 × 2
→ 0 = 0
- For natural number
Addition
→ a = 2 and b = 1
→ 2 + 1 = 1 + 2
→ 3 = 3
Multiplication
→ a = 2 and b = 1
→ 2 × 1 = 1 × 2
→ 2 × 2
According to the Associative property
Addition : (a + b) + c = a + (b + c)
Multiplication : (a × b) × c = a × (b × c)
★ Point to be noted
Associative property is not applicable for division and subtraction.
- For rational number
Addition
→ a = 2/3, b = 1/2 and c = 2/5
→ (2/3 + 1/2) + 2/5 = 2/3 + (1/2 + 2/5)
→ (4 + 3/6) + 2/5 = 2/3 + (5 + 4/10)
→ 7/6 + 2/5 = 2/3 + 9/10
→ 35 + 12/30 = 20 + 27/30
→ 47/30 = 47/30
Multiplication
→ a = 2/3, b = 1/2 and c = 2/5
→ (2/3 × 1/2) × 2/5 = 2/3 × (1/2 × 2/5)
→ 1/3 × 2/5 = 2/3 × 1/5
→ 2/15 = 2/15
- For integer
Addition
→ a = 2 , b = - 3 and c = - 1
→ [ 2 + (-3) ] + (-1) = 2 + [(-3) + (-1) ]
→ [2 - 3] - 1 = 2 + [-3 - 1]
→ - 1 - 1 = 2 - 4
→ - 2 = -2
Multiplication
→ a = 2, b = - 3 and c = - 1
→ [ 2 × (-3) ] × (-1) = 2 × [(-3) × (-1) ]
→ -6 × (-1) = 2 × 3
→ 6 = 6
- For whole number
Addition
→ a = 2, b = 0 and c = 3
→ (2 + 0) + 3 = 2 + (0+3)
→ 2 + 3 = 2 + 3
→ 5 = 5
Multiplication
→ a = 2, b = 0 and c = 3
→ (2 × 0) × 3 = (2×0) × 3
→ 0 × 3 = 0 × 3
→ 0 = 0
- For natural number
Addition
→ a = 2, b = 1 and c = 5
→ (2 + 1) + 5 = 2 + (1+5)
→ 3 + 5 = 2 + 6
→ 8 = 8
Multiplication
→ a = 2, b = 1 and c = 5
→ (2 × 1) × 5 = 2 × (1 × 5)
→ 2 × 5 = 2 × 5
→ 10 = 10
- Hence, proved